The sport and stadium specialist will work with the same consortium that produced the Emirates Stadium and is working on the Olympic centrepiece.
The proposals (below) will centre around a new 35,000-seat venue for rugby, football and Gaelic sports and will 'provide a landmark venue for Northern Ireland'.
It will be next to a conflict-resolution centre, which will also be on the former prison site.
John Barrow, senior principal at HOK Sport said: 'Our ideas are at a very early stage, but our vision is for a world-class stadium for world-class supporters - the people of Northern Ireland.
'This will be a stadium where every seat in the house is the best seat, and one which will be an exemplar for comfort, safety, accessibility and sustainability.'
Demolition of the prison is expected to take place imminently, although the stadium plans will not win the green light formally until later this year.